Such systems are of interest to researchers because they are systems with energy dissipation.
There is compression of the volume of the phase space in them, and all trajectories are uniformly bounded. Thus, there is an attracting set called the attractor of the dynamical system to which all solutions tend at \(t\rightarrow \infty \) .
Consequently, the attractors of dissipative systems determine their behavior over long time intervals. However, for many systems of the form (REF ), the limit solutions are unstable. Therefore,
correct numerical integration requires the high-precision methods that make it possible to flexibly control the accumulation of calculation errors over a long time interval. For example, with an increase of the order of the Runge–Kutta methods, the complexity of the formulas for calculating the approximate values of the phase coordinates (they have a tree structure) [1]}, [2]} grows.
